US6411979B1 - Complex number multiplier circuit - Google Patents
Complex number multiplier circuit Download PDFInfo
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- US6411979B1 US6411979B1 US09/333,071 US33307199A US6411979B1 US 6411979 B1 US6411979 B1 US 6411979B1 US 33307199 A US33307199 A US 33307199A US 6411979 B1 US6411979 B1 US 6411979B1
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- 239000013598 vector Substances 0.000 claims abstract description 26
- 239000000047 product Substances 0.000 description 53
- 241001442055 Vipera berus Species 0.000 description 21
- 238000010586 diagram Methods 0.000 description 9
- 238000000034 method Methods 0.000 description 7
- 238000007792 addition Methods 0.000 description 5
- 230000000295 complement effect Effects 0.000 description 4
- 238000003491 array Methods 0.000 description 3
- 239000011159 matrix material Substances 0.000 description 3
- 230000003044 adaptive effect Effects 0.000 description 2
- 230000008901 benefit Effects 0.000 description 2
- 238000004364 calculation method Methods 0.000 description 2
- 239000012467 final product Substances 0.000 description 2
- 230000009466 transformation Effects 0.000 description 2
- 238000000354 decomposition reaction Methods 0.000 description 1
- 235000019800 disodium phosphate Nutrition 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 230000005855 radiation Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
- G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
- G06F7/4806—Computations with complex numbers
- G06F7/4812—Complex multiplication
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
- G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
- G06F7/52—Multiplying; Dividing
- G06F7/523—Multiplying only
- G06F7/533—Reduction of the number of iteration steps or stages, e.g. using the Booth algorithm, log-sum, odd-even
- G06F7/5334—Reduction of the number of iteration steps or stages, e.g. using the Booth algorithm, log-sum, odd-even by using multiple bit scanning, i.e. by decoding groups of successive multiplier bits in order to select an appropriate precalculated multiple of the multiplicand as a partial product
- G06F7/5336—Reduction of the number of iteration steps or stages, e.g. using the Booth algorithm, log-sum, odd-even by using multiple bit scanning, i.e. by decoding groups of successive multiplier bits in order to select an appropriate precalculated multiple of the multiplicand as a partial product overlapped, i.e. with successive bitgroups sharing one or more bits being recoded into signed digit representation, e.g. using the Modified Booth Algorithm
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- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Theoretical Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Complex Calculations (AREA)
Abstract
Description
TABLE 1 | |||
Quintuplet | Quintuplet | ||
Value | Signed Digit Value | Value | Signed Digit Value |
00000 | +0 | 10000 | −8 |
00001 | +1 | 10001 | −7 |
00010 | +1 | 10010 | −7 |
00011 | +2 | 10011 | −6 |
00100 | +2 | 10100 | −6 |
00101 | +3 | 10101 | −5 |
00110 | +3 | 10110 | −5 |
00111 | +4 | 10111 | −4 |
01000 | +4 | 11000 | −4 |
01001 | +5 | 11001 | −3 |
01010 | +5 | 11010 | −3 |
01011 | +6 | 11011 | −2 |
01100 | +6 | 11100 | −2 |
01101 | +7 | 11101 | −1 |
01110 | +7 | 11110 | −1 |
01111 | +8 | 11111 | 0 |
TABLE 2 | |||
Y1R | Y1I | ||
X1R | X1R Y1R | X1R Y1I | ||
X1I | X1I Y1R | X1I Y1I | ||
TABLE 3 | |||||
Y1R | Y1I | Y2R | Y2I | ||
X1R | X1RY1R | X1RY1I | X1RY2R | X1RY2I | ||
X1I | X1IY1R | X1IY1I | X1IY2R | X1IY2I | ||
X2R | X2RY1R | X2RY1I | X2RY2R | X2RY2I | ||
X2I | X2IY1R | X2IY1I | X2IY2R | X2IY2I | ||
Claims (6)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US09/333,071 US6411979B1 (en) | 1999-06-14 | 1999-06-14 | Complex number multiplier circuit |
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US09/333,071 US6411979B1 (en) | 1999-06-14 | 1999-06-14 | Complex number multiplier circuit |
Publications (1)
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US6411979B1 true US6411979B1 (en) | 2002-06-25 |
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US09/333,071 Expired - Lifetime US6411979B1 (en) | 1999-06-14 | 1999-06-14 | Complex number multiplier circuit |
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Cited By (17)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20020169813A1 (en) * | 2000-11-01 | 2002-11-14 | Bops, Inc. | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation |
US20030009502A1 (en) * | 2001-06-29 | 2003-01-09 | Nec Corporation | Complex vector operation processor with pipeline processing function and system using the same |
US20030046323A1 (en) * | 2001-03-31 | 2003-03-06 | Orchard John T. | Architecture and related methods for efficiently performing complex arithmetic |
US6622154B1 (en) * | 1999-12-21 | 2003-09-16 | Lsi Logic Corporation | Alternate booth partial product generation for a hardware multiplier |
US20030225809A1 (en) * | 2002-05-28 | 2003-12-04 | Interdigital Technology Corporation | Dual use dual complex multiplier and complex divider |
US6675187B1 (en) * | 1999-06-10 | 2004-01-06 | Agere Systems Inc. | Pipelined linear array of processor elements for performing matrix computations |
US6826587B1 (en) * | 1999-05-20 | 2004-11-30 | FRANCE TéLéCOM | Complex number multiplier |
WO2006013487A1 (en) * | 2004-07-29 | 2006-02-09 | Koninklijke Philips Electronics N.V. | Complex signal scaling for phase and/or amplitude modulated signals |
US7401054B1 (en) | 2001-03-26 | 2008-07-15 | Accenture Gmbh | Content bank for objects |
US20090077154A1 (en) * | 2007-09-18 | 2009-03-19 | Nec Electronics Corporation | Microprocessor |
US20120166511A1 (en) * | 2010-12-22 | 2012-06-28 | Hiremath Chetan D | System, apparatus, and method for improved efficiency of execution in signal processing algorithms |
US8572153B1 (en) * | 2004-12-16 | 2013-10-29 | Xilinx, Inc. | Multiplier circuit configurable for real or complex operation |
US8943114B2 (en) | 2011-08-17 | 2015-01-27 | Avago Technologies General Ip (Singapore) Pte. Ltd. | Method for implementing 32 bit complex multiplication by using 16-bit complex multipliers |
US9778905B1 (en) * | 2016-01-13 | 2017-10-03 | Xilinx, Inc. | Multiplier circuits configurable for real or complex operation |
EP3280069A1 (en) * | 2016-08-01 | 2018-02-07 | Space Systems/Loral, LLC | A beamforming system and method |
US10559880B1 (en) * | 2016-04-25 | 2020-02-11 | Avago Technologies International Sales Pte. Limited | Multi-layered hybrid beamforming |
WO2022057240A1 (en) * | 2020-09-18 | 2022-03-24 | 江苏科技大学 | Sound field perception-based low-power acoustic proximity alarm apparatus and alarm method |
Citations (7)
Publication number | Priority date | Publication date | Assignee | Title |
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US5262976A (en) * | 1989-11-13 | 1993-11-16 | Harris Corporation | Plural-bit recoding multiplier |
US5694349A (en) * | 1996-03-29 | 1997-12-02 | Amati Communications Corp. | Low power parallel multiplier for complex numbers |
US5777915A (en) * | 1993-05-21 | 1998-07-07 | Deutsche Itt Industries Gmbh | Multiplier apparatus and method for real or complex numbers |
US6038583A (en) * | 1997-10-23 | 2000-03-14 | Advanced Micro Devices, Inc. | Method and apparatus for simultaneously multiplying two or more independent pairs of operands and calculating a rounded products |
US6122654A (en) * | 1997-04-28 | 2000-09-19 | Yozan Inc. | Complex multiplication circuit |
US6237016B1 (en) * | 1995-09-05 | 2001-05-22 | Intel Corporation | Method and apparatus for multiplying and accumulating data samples and complex coefficients |
US6272512B1 (en) * | 1998-10-12 | 2001-08-07 | Intel Corporation | Data manipulation instruction for enhancing value and efficiency of complex arithmetic |
-
1999
- 1999-06-14 US US09/333,071 patent/US6411979B1/en not_active Expired - Lifetime
Patent Citations (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5262976A (en) * | 1989-11-13 | 1993-11-16 | Harris Corporation | Plural-bit recoding multiplier |
US5777915A (en) * | 1993-05-21 | 1998-07-07 | Deutsche Itt Industries Gmbh | Multiplier apparatus and method for real or complex numbers |
US6237016B1 (en) * | 1995-09-05 | 2001-05-22 | Intel Corporation | Method and apparatus for multiplying and accumulating data samples and complex coefficients |
US5694349A (en) * | 1996-03-29 | 1997-12-02 | Amati Communications Corp. | Low power parallel multiplier for complex numbers |
US6122654A (en) * | 1997-04-28 | 2000-09-19 | Yozan Inc. | Complex multiplication circuit |
US6038583A (en) * | 1997-10-23 | 2000-03-14 | Advanced Micro Devices, Inc. | Method and apparatus for simultaneously multiplying two or more independent pairs of operands and calculating a rounded products |
US6272512B1 (en) * | 1998-10-12 | 2001-08-07 | Intel Corporation | Data manipulation instruction for enhancing value and efficiency of complex arithmetic |
Cited By (35)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
USRE40803E1 (en) * | 1999-05-20 | 2009-06-23 | Fahrenheit Thermoscope Llc | Complex number multiplier |
US6826587B1 (en) * | 1999-05-20 | 2004-11-30 | FRANCE TéLéCOM | Complex number multiplier |
US6675187B1 (en) * | 1999-06-10 | 2004-01-06 | Agere Systems Inc. | Pipelined linear array of processor elements for performing matrix computations |
US6622154B1 (en) * | 1999-12-21 | 2003-09-16 | Lsi Logic Corporation | Alternate booth partial product generation for a hardware multiplier |
US20060224656A1 (en) * | 2000-11-01 | 2006-10-05 | Pts Corporation | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation |
US7072929B2 (en) * | 2000-11-01 | 2006-07-04 | Pts Corporation | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation |
US20100121899A1 (en) * | 2000-11-01 | 2010-05-13 | Altera Corporation | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation |
US20020169813A1 (en) * | 2000-11-01 | 2002-11-14 | Bops, Inc. | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation |
US7680873B2 (en) * | 2000-11-01 | 2010-03-16 | Altera Corporation | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation |
US8335812B2 (en) * | 2000-11-01 | 2012-12-18 | Altera Corporation | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation |
US20080243915A1 (en) * | 2001-03-26 | 2008-10-02 | Baiju Shah | Content bank for objects |
US7401054B1 (en) | 2001-03-26 | 2008-07-15 | Accenture Gmbh | Content bank for objects |
US20080243873A1 (en) * | 2001-03-26 | 2008-10-02 | Baiju Shah | Content bank for objects |
US20030046323A1 (en) * | 2001-03-31 | 2003-03-06 | Orchard John T. | Architecture and related methods for efficiently performing complex arithmetic |
US20030009502A1 (en) * | 2001-06-29 | 2003-01-09 | Nec Corporation | Complex vector operation processor with pipeline processing function and system using the same |
US7051061B2 (en) | 2002-05-28 | 2006-05-23 | Interdigital Technology Corporation | Dual use dual complex multiplier and complex divider |
US20030225809A1 (en) * | 2002-05-28 | 2003-12-04 | Interdigital Technology Corporation | Dual use dual complex multiplier and complex divider |
US20040139140A1 (en) * | 2002-05-28 | 2004-07-15 | Interdigital Technology Corporation | Dual use dual complex multiplier and complex divider |
US6691144B2 (en) * | 2002-05-28 | 2004-02-10 | Interdigital Technology Corporation | Dual use dual complex multiplier and complex divider |
CN1993958B (en) * | 2004-07-29 | 2012-06-27 | Nxp股份有限公司 | Complex signal scaling for phase and/or amplitude modulated signals |
US20090175380A1 (en) * | 2004-07-29 | 2009-07-09 | Koninklijke Philips Electronics N.V. | Complex Signal Scaling for Phase and/or Amplitude Modulated Signals |
US7991076B2 (en) | 2004-07-29 | 2011-08-02 | St-Ericsson Sa | Complex signal scaling for phase and/or amplitude modulated signals |
JP4868319B2 (en) * | 2004-07-29 | 2012-02-01 | エスティー‐エリクソン、ソシエテ、アノニム | Complex signal scaling for phase and / or amplitude modulated signals |
WO2006013487A1 (en) * | 2004-07-29 | 2006-02-09 | Koninklijke Philips Electronics N.V. | Complex signal scaling for phase and/or amplitude modulated signals |
US8572153B1 (en) * | 2004-12-16 | 2013-10-29 | Xilinx, Inc. | Multiplier circuit configurable for real or complex operation |
US8271571B2 (en) * | 2007-09-18 | 2012-09-18 | Renesas Electronics Corporation | Microprocessor |
US20090077154A1 (en) * | 2007-09-18 | 2009-03-19 | Nec Electronics Corporation | Microprocessor |
JP2009075676A (en) * | 2007-09-18 | 2009-04-09 | Nec Electronics Corp | Microprocessor |
US20120166511A1 (en) * | 2010-12-22 | 2012-06-28 | Hiremath Chetan D | System, apparatus, and method for improved efficiency of execution in signal processing algorithms |
US8943114B2 (en) | 2011-08-17 | 2015-01-27 | Avago Technologies General Ip (Singapore) Pte. Ltd. | Method for implementing 32 bit complex multiplication by using 16-bit complex multipliers |
US9778905B1 (en) * | 2016-01-13 | 2017-10-03 | Xilinx, Inc. | Multiplier circuits configurable for real or complex operation |
US10559880B1 (en) * | 2016-04-25 | 2020-02-11 | Avago Technologies International Sales Pte. Limited | Multi-layered hybrid beamforming |
EP3280069A1 (en) * | 2016-08-01 | 2018-02-07 | Space Systems/Loral, LLC | A beamforming system and method |
US9917623B1 (en) | 2016-08-01 | 2018-03-13 | Space Systems/Loral, Llc | Digital beamforming architecture |
WO2022057240A1 (en) * | 2020-09-18 | 2022-03-24 | 江苏科技大学 | Sound field perception-based low-power acoustic proximity alarm apparatus and alarm method |
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